Electromagnetic theory miscellaneous


Electromagnetic theory miscellaneous

Electromagnetic Theory

  1. The velocity of the plane wave esin2(ωt – βx) is—









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    The wave is

    esin2(ωt − βx) = esin2β
    ω
    t − x
    t

    When the argument is reduced to the form kt – x, the coefficient of t is the velocity of propagation. Hence, the velocity of the wave is ω/β.

    Correct Option: D

    The wave is

    esin2(ωt − βx) = esin2β
    ω
    t − x
    t

    When the argument is reduced to the form kt – x, the coefficient of t is the velocity of propagation. Hence, the velocity of the wave is ω/β.


  1. The frequency of the power wave associated with an electromagnetic wave having an E field as
    E = e– z/ δ cos (ωt – z/δ),
    is given by—









  1. View Hint View Answer Discuss in Forum

    E = e– z/δ cos (ωt – z/δ)
    The radian frequency of E wave is ω, same would be the radian frequency of associated H wave. The frequency of power wave is double the corresponding frequency of E or H wave. Thus the radian frequency is 2 ω and cyclic frequency 2ω/ 2π = ω/ π.

    Correct Option: D

    E = e– z/δ cos (ωt – z/δ)
    The radian frequency of E wave is ω, same would be the radian frequency of associated H wave. The frequency of power wave is double the corresponding frequency of E or H wave. Thus the radian frequency is 2 ω and cyclic frequency 2ω/ 2π = ω/ π.



  1. A plane electromagnetic wave in free space is specified by the electric field
    E = ax [20 cos (ωt – βz) + 5 cos (ωt + βz)] V/m.
    The associated magnetic field is—









  1. View Hint View Answer Discuss in Forum

    E and H are related by η
    i.e. E/ H = η,
    the characteristic impedance of the medium which is 120 π for free space. Also, phase of H in the reflected component of the wave has to reverse so that travelling of the reflected wave is correctly given by the direction of E × H.
    Of course, E × H are perpendicular to each other in the incident component or the forward travelling component of the wave. Keeping in view the above facts and the given expression for E.
    H = ay (1/ 120 π) 20 cos (ωt – βz) – 5 cos (ωt + βz) A /m.

    Correct Option: C

    E and H are related by η
    i.e. E/ H = η,
    the characteristic impedance of the medium which is 120 π for free space. Also, phase of H in the reflected component of the wave has to reverse so that travelling of the reflected wave is correctly given by the direction of E × H.
    Of course, E × H are perpendicular to each other in the incident component or the forward travelling component of the wave. Keeping in view the above facts and the given expression for E.
    H = ay (1/ 120 π) 20 cos (ωt – βz) – 5 cos (ωt + βz) A /m.


  1. The maximum usable frequency of an ionospheric layer at 60º incidance and with 8 MHz. The critical frequency is—









  1. View Hint View Answer Discuss in Forum

    Maximum usable frequency, muf = fc sec θ
    where, given θ i = 60º
    fc = 8 MHz
    Now, muf = 8 × 106 × sec 60º
    = 16 MHz

    Correct Option: A

    Maximum usable frequency, muf = fc sec θ
    where, given θ i = 60º
    fc = 8 MHz
    Now, muf = 8 × 106 × sec 60º
    = 16 MHz



  1. The potential difference between the forces A and B of a uniformly polarized infinite slab shown in the figure is—









  1. View Hint View Answer Discuss in Forum

    D = ∈0 E + P also D = ∈0r E
    ∴    

    0r E = ∈0 E + P or E =
    P
    0(∈r − 1)

    ∴    
    Potential difference V = Ed =
    Pd
    0(∈r − 1)

    Correct Option: A

    D = ∈0 E + P also D = ∈0r E
    ∴    

    0r E = ∈0 E + P or E =
    P
    0(∈r − 1)

    ∴    
    Potential difference V = Ed =
    Pd
    0(∈r − 1)